The Best-Fit Line. Linear Regression. How do you determine the best-fit line through data points?. Fortunately technology, such as the graphing calculator and Excel, can do a better job than your eye and a ruler!. y-variable. x-variable. The Equation of a Straight Line. y = mx + b
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such as the graphing calculator
and Excel, can do a better
job than your eye and a ruler!
y = mx + b
where m is the slope or Dy/Dx and b is the y-intercept
In some physical settings, b = 0 so the equation simplifies to:
y = mx
the sum of the squared deviations
y = mx + b
deviation = residual
= ydata point – yequation
r2 is high
Goodness of Fit: Using r2
How about the value of r2?
99.1% of the y-variation is due to
the variation of the x-variable
Only 82% of the y-variation is due to
the variation of the x-variable - what
is the other 18% caused by?
make a difference?
Using the set intercept = 0 option
lowers the r2 value by a small amount
and changes the slope slightly
A = mc
A = 0.89c
99.1% of the variation of the absorbance is due to the variation of the concentration.